My question is in regards to the minimization of a convex function where the feasible set of solutions is non-convex. Can projected gradient descent (PGD) be used here to obtain a stationary solution?

By PGD, I am referring to the process of stepping in the negative direction of the gradient and then projecting the current solution unto the feasible set. Let's assume that the projector unto the non-convex set exists and is unique.